A cyclist and a motorcyclist left town A for town B. The speed of the bike is 10 km / h

A cyclist and a motorcyclist left town A for town B. The speed of the bike is 10 km / h less than the speed of the motorcyclist, so he spent 6 hours more for the whole journey. How fast was the motorcyclist driving if the distance between cities was 120 km?

Decision:

1. Let’s take the speed of the motorcyclist as x, then the speed of the cyclist x – 10.

2. The time of the motorcyclist on the way will be taken as t. Then the cyclist spent t + 6 hours for the entire journey.

3. We can make 2 equations:

a) x * t = 120;

b) (x – 10) * (t + 6) = 120.

4. Express t in terms of x using the first equation:

t = 120 / x.

5. Substitute the resulting equation into the second:

(x – 10) * (120 / x + 6) = 120;

120x / x + 6x -1200 / x – 60 = 120;

x ^ 2 – 10x -200 = 0;

6. Solve the quadratic equation:

D = 100 +800 = 900:

x1 = (10 + 30) / 2 = 20;

x2 = (10 – 30) / 2 = -10.

Since the speed cannot be negative, the correct answer is x1.

Answer: The speed of the motorcyclist is 20 km / h.